On Wednesday afternoon, between the geography lesson on ancient Egypt’s hand-operated irrigation system and an art project that involved drawing a model city next to a mountain, our fourth-grade teacher, Mr. Hibler, developed a cough. This cough began with a series of muffled throat-clearings and progressed to propulsive noises contained within Mr. Hibler’s closed mouth. “Listen to him,” Carol Peterson whispered to me. “He’s gonna blow up.” Mr. Hibler’s laughter—dazed and infrequent—sounded a bit like his cough, but as we worked on our model cities we would look up, thinking he was enjoying a joke, and see Mr. Hibler’s face turning red, his cheeks puffed out. This was not laughter. Twice he bent over, and his loose tie, like a plumb line, hung down straight from his neck as he exploded himself into a Kleenex. He would excuse himself, then go on coughing. “I’ll bet you a dime,” Carol Peterson whispered, “we get a substitute tomorrow.”

Carol sat at the desk in front of mine and was a bad person—when she thought no one was looking she would blow her nose on notebook paper, then crumple it up and throw it into the wastebasket—but at times of crisis she spoke the truth. I knew I’d lose the dime.

“No deal,” I said.

When Mr. Hibler stood us in formation at the door just prior to the final bell, he was almost incapable of speech. “I’m sorry, boys and girls,” he said. “I seem to be coming down with something.”

“I hope you feel better tomorrow, Mr. Hibler,” Bobby Kryzanowicz, the faultless brown-noser, said, and I heard Carol Peterson’s evil giggle. Then Mr. Hibler opened the door and we walked out to the buses, a clique of us starting noisily to hawk and laugh as soon as we thought we were a few feet beyond Mr. Hibler’s earshot.

Since Five Oaks was a rural community, and in Michigan, the supply of substitute teachers was limited to the town’s unemployed community college graduates, a pool of about four mothers. These ladies fluttered, provided easeful class days, and nervously covered material we had mastered weeks earlier. Therefore it was a surprise when a woman we had never seen came into the class the next day, carrying a purple purse, a checkerboard lunchbox, and a few books. She put the books on one side of Mr. Hibler’s desk and the lunchbox on the other, next to the Voice of Music phonograph. Three of us in the back of the room were playing with Heever, the chameleon that lived in a terrarium and on one of the plastic drapes, when she walked in.

She clapped her hands at us. “Little boys,” she said, “why are you bent over together like that?” She didn’t wait for us to answer. “Are you tormenting an animal? Put it back. Please sit down at your desks. I want no cabals this time of the day.” We just stared at her. “Boys,” she repeated, “I asked you to sit down.”

I put the chameleon in his terrarium and felt my way to my desk, never taking my eyes off the woman. With white and green chalk, she had started to draw a tree on the left side of the blackboard. She didn’t look usual. Furthermore, her tree was outsized, disproportionate, for some reason.

“This room needs a tree,” she said, with one line drawing the suggestion of a leaf. “A large, leafy, shady, deciduous . . . oak.”

Her fine, light hair had been done up in what I would learn years later was called a chignon, and she wore gold-rimmed glasses whose lenses seemed to have the faintest blue tint. Harold Knardahl, who sat across from me, whispered, “Mars,” and I nodded slowly, savoring the imminent weirdness of the day. The substitute drew another branch with an extravagant arm gesture, then turned around and said, “Good morning. I don’t believe I said good morning to all of you yet.”

Facing us, she was no special age—an adult is an adult—but her face had two prominent lines, descending vertically from the sides of her mouth to her chin. I knew where I had seen those lines before: Pinocchio. They were marionette lines. “You may stare at me,” she said to us, as a few more kids from the last bus came into the room, their eyes fixed on her, “for a few more seconds, until the bell rings. Then I will permit no more staring. Looking I will permit. Staring, no. It is impolite to stare, and a sign of bad breeding. You cannot make a social effort while staring.”

Harold Knardahl did not glance at me, or nudge, but I heard him whisper “Mars” again, trying to get more mileage out of his single joke with the kids who had just come in.

When everyone was seated, the substitute teacher finished her tree, put down her chalk fastidiously on the phonograph, brushed her hands, and faced us. “Good morning,” she said. “I am Miss Ferenczi, your teacher for the day. I am fairly new to your community, and I don’t believe any of you know me. I will therefore start by telling you a story about myself.”

While we settled back, she launched into her tale. She said her grandfather had been a Hungarian prince; her mother had been born in some place called Flanders, had been a pianist, and had played concerts for people Miss Ferenczi referred to as “crowned heads.” She gave us a knowing look. “Grieg,” she said, “the Norwegian master, wrote a concerto for piano that was . . . ”—she paused—“my mother’s triumph at her debut concert in London.” Her eyes searched the ceiling. Our eyes followed. Nothing up there but ceiling tile. “For reasons that I shall not go into, my family’s fortunes took us to Detroit, then north to dreadful Saginaw, and now here I am in Five Oaks, as your substitute teacher, for today, Thursday, October the eleventh. I believe it will be a good day: all the forecasts coincide. We shall start with your reading lesson. Take out your reading book. I believe it is called Broad Horizons, or something along those lines.”

Jeannie Vermeesch raised her hand. Miss Ferenczi nodded at her. “Mr. Hibler always starts the day with the Pledge of Allegiance,” Jeannie whined.

“Oh, does he? In that case,” Miss Ferenczi said, “you must know it very well by now, and we certainly need not spend our time on it. No, no allegiance pledging on the premises today, by my reckoning. Not with so much sunlight coming into the room. A pledge does not suit my mood.” She glanced at her watch. “Time is flying. Take out Broad Horizons.”

She disappointed us by giving us an ordinary lesson, complete with vocabulary and drills, comprehension questions, and recitation. She didn’t seem to care for the material, however. She sighed every few minutes and rubbed her glasses with a frilly handkerchief that she withdrew, magician-style, from her left sleeve.

After reading we moved on to arithmetic. It was my favorite time of the morning, when the lazy autumn sunlight dazzled its way through ribbons of clouds past the windows on the east side of the classroom and crept across the linoleum floor. On the playground the first group of children, the kindergartners, were running on the quack grass just beyond the monkey bars. We were doing multiplication tables. Miss Ferenczi had made John Wazny stand up at his desk in the front row. He was supposed to go through the tables of six. From where I was sitting, I could smell the Vitalis soaked into John’s plastered hair. He was doing fine until he came to six times eleven and six times twelve. “Six times eleven,” he said, “is sixty-eight. Six times twelve is . . . ” He put his fingers to his head, quickly and secretly sniffed his fingertips, and said, “ . . . seventy-two.” Then he sat down.

“Fine,” Miss Ferenczi said. “Well now. That was very good.”

“Miss Ferenczi!” One of the Eddy twins was waving her hand desperately in the air. “Miss Ferenczi! Miss Ferenczi!”

“Yes?”

“John said that six times eleven is sixty-eight and you said he was right!”

“Did I?” She gazed at the class with a jolly look breaking across her marionette’s face. “Did I say that? Well, what is six times eleven?”

“It’s sixty-six!”

She nodded. “Yes. So it is. But, and I know some people will not entirely agree with me, at some times it is sixty-eight.”

“When? When is it sixty-eight?”

We were all waiting.

“In higher mathematics, which you children do not yet understand, six times eleven can be considered to be sixty-eight.” She laughed through her nose. “In higher mathematics numbers are . . . more fluid. The only thing a number does is contain a certain amount of something. Think of water. A cup is not the only way to measure a certain amount of water, is it?” We were staring, shaking our heads. “You could use saucepans or thimbles. In either case, the water would be the same. Perhaps,” she started again, “it would be better for you to think that six times eleven is sixty-eight only when I am in the room.”

“Why is it sixty-eight,” Mark Poole asked, “when you’re in the room?”

“Because it’s more interesting that way,” she said, smiling very rapidly behind her blue-tinted glasses. “Besides, I’m your substitute teacher, am I not?” We all nodded. “Well, then, think of six times eleven equals sixty-eight as a substitute fact.”

“A substitute fact?”

“Yes.” Then she looked at us carefully. “Do you think,” she asked, “that anyone is going to be hurt by a substitute fact?”

We looked back at her.

“Will the plants on the windowsill be hurt?” We glanced at them. There were sensitive plants thriving in a green plastic tray, and several wilted ferns in small clay pots. “Your dogs and cats, or your moms and dads?” She waited. “So,” she concluded, “what’s the problem?”

“But it’s wrong,” Janice Weber said, “isn’t it?”

“What’s your name, young lady?”

“Janice Weber.”

“And you think it’s wrong, Janice?”

“I was just asking.”

“Well, all right. You were just asking. I think we’ve spent enough time on this matter by now, don’t you, class? You are free to think what you like. When your teacher, Mr. Hibler, returns, six times eleven will be sixty-six again, you can rest assured. And it will be that for the rest of your lives in Five Oaks. Too bad, eh?” She raised her eyebrows and glinted herself at us. “But for now, it wasn’t. So much for that. Let us go on to your assigned problems for today, as painstakingly outlined, I see, in Mr. Hibler’s lesson plan. Take out a sheet of paper and write your names on the upper left-hand corner.”

For the next half hour we did the rest of our arithmetic problems. We handed them in and then went on to spelling, my worst subject. Spelling always came before lunch. We were taking spelling dictation and looking at the clock. “Thorough,” Miss Ferenczi said. “Boundary.” She walked in the aisles between the desks, holding the spelling book open and looking down at our papers. “Balcony.” I clutched my pencil. Somehow, the way she said those words, they seemed foreign, mis-voweled and mis-consonated. I stared down at what I had spelled. Balconie. I turned the pencil upside down and erased my mistake. Balconey. That looked better, but still incorrect. I cursed the world of spelling and tried erasing it again and saw the paper beginning to wear away. Balkony. Suddenly I felt a hand on my shoulder.

“I don’t like that word either,” Miss Ferenczi whispered, bent over, her mouth near my ear. “It’s ugly. My feeling is, if you don’t like a word, you don’t have to use it.” She straightened up, leaving behind a slight odor of Clorets.

At lunchtime we went out to get our trays of sloppy joes, peaches in heavy syrup, coconut cookies, and milk, and brought them back to the classroom, where Miss Ferenczi was sitting at the desk, eating a brown sticky thing she had unwrapped from tightly rubber-banded waxed paper. “Miss Ferenczi,” I said, raising my hand. “You don’t have to eat with us. You can eat with the other teachers. There’s a teacher’s lounge,” I ended up, “next to the principal’s office.”

“No, thank you,” she said. “I prefer it here.”

“We’ve got a room monitor,” I said. “Mrs. Eddy.” I pointed to where Mrs. Eddy, Joyce and Judy’s mother, sat silently at the back of the room, doing her knitting.

“That’s fine,” Miss Ferenczi said. “But I shall continue to eat here, with you children. I prefer it,” she repeated.

“How come?” Wayne Razmer asked without raising his hand.

“I talked to the other teachers before class this morning,” Miss Ferenczi said, biting into her brown food. “There was a great rattling of the words for the fewness of the ideas. I didn’t care for their brand of hilarity. I don’t like ditto-machine jokes.”

“It most certainly is food. It’s a stuffed fig. I had to drive almost down to Detroit to get it. I also brought some smoked sturgeon. And this,” she said, lifting some green leaves out of her lunchbox, “is raw spinach, cleaned this morning.”

“Why’re you eating raw spinach?” Maxine asked.

“It’s good for you,” Miss Ferenczi said. “More stimulating than soda pop or smelling salts.” I bit into my sloppy joe and stared blankly out the window. An almost invisible moon was faintly silvered in the daytime autumn sky. “As far as food is concerned,” Miss Ferenczi was saying, “you have to shuffle the pack. Mix it up. Too many people eat . . . well, never mind.”

“Miss Ferenczi,” Carol Peterson said, “what are we going to do this afternoon?”

“Well,” she said, looking down at Mr. Hibler’s lesson plan, “I see that your teacher, Mr. Hibler, has you scheduled for a unit on the Egyptians.” Carol groaned. “Yessss,” Miss Ferenczi continued, “that is what we will do: the Egyptians. A remarkable people. Almost as remarkable as the Americans. But not quite.” She lowered her head, did her quick smile, and went back to eating her spinach.